The irreducible components of the moduli space of dihedral covers of algebraic curves | Zendy

Fabrizio Catanese | Zendy; Michael Lönne | Zendy; Fabio Perroni | Zendy

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The irreducible components of the moduli space of dihedral covers of algebraic curves

Author(s) -

Fabrizio Catanese,

Michael Lönne,

Fabio Perroni

Publication year - 2015

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/338

Subject(s) - mathematics , moduli space , pure mathematics , irreducible component , moduli of algebraic curves , moduli , algebraic number , dihedral group , dihedral angle , space (punctuation) , algebraic curve , algebra over a field , mathematical analysis , group (periodic table) , differential algebraic equation , ordinary differential equation , hydrogen bond , chemistry , physics , quantum mechanics , molecule , differential equation , linguistics , philosophy , organic chemistry

In this paper we introduce a new invariant for the action of a finite group G on a compact complex curve of genus g. With the aid of this invariant we achieve the classification of the components of the moduli space of curves with an effective action by the dihedral group Dn. This invariant has been used in the meanwhile by the authors in order to extend the genus stabilization result of Livingston and Dunfield and Thurston to the ramified case. This new version contains an appendix clarifying the correspondence between the above components and the image loci in the moduli space M_g (classifying when two such components have the same image)

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